A systematic derivative expansion of the adiabatic phase

Theoretical Physics

Carl M. Bender, N. Papanicolaou

Berry discovered that wave functions may acquire a geometrical phase factor, in addition to the usual dynamical phase, during an adiabatic cycle with period T. The dynamical and Berry phases are here recognized as the first two terms in a systematic WKB expansion in powers of ε = 1/ T. We thus provide a simple method for the calculation of adiabatic phases and for a consistent inclusion of nonadiabatic corrections.

Jonas Larson, Erik Sjöqvist, Patrik Öhberg

Stefan Teufel

I. L. Egusquiza

We restate the adiabatic elimination approximation as the first term in a singular perturbation expansion. We use the invariant manifold formalism for singular perturbations in dynamical systems to identify systematic improvements on adiabatic elimination, connecting with well established quantum mechanical perturbation methods. We prove convergence of the expansions when energy scales are well separated. We state and solve the problem of hermiticity of improved effective hamiltonians.

L. Navarro, L. M. Garrido